Cheerlessness is the noun for that grey, joyless quality — the cheerlessness of a wet Monday, or of a room with no colour and no welcome. It comes straight from cheerless. It is a heavy, formal word. Almost nobody says it in ordinary conversation; they would say how gloomy or depressing something felt. You will meet it in books more than in talk. The meaning is the same as cheerless, only named as a thing: not “the place is cheerless,” but “the cheerlessness of the place.”